Related papers: Periodic trawl processes: Simulation, statistical …
Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review…
In this work we derive limit theorems for trawl processes. First,we study the asymptotic behaviour of the partial sums of the discretized trawl process $(X_{i\Delta_{n}})_{i=0}^{\lfloor nt\rfloor-1}$, under the assumption that as…
We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions,…
Temporal logic inference is the process of extracting formal descriptions of system behaviors from data in the form of temporal logic formulas. The existing temporal logic inference methods mostly neglect uncertainties in the data, which…
Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options:…
Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
In this paper, we prove measurability of event for which a general continuous-time stochastic process satisfies continuous-time Metric Temporal Logic (MTL) formula. Continuous-time MTL can define temporal constrains for physical system in…
We describe a new class of self-similar symmetric $\alpha$-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting…
Temporal point process (TPP) models combined with recurrent neural networks provide a powerful framework for modeling continuous-time event data. While such models are flexible, they are inherently sequential and therefore cannot benefit…
A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
In this paper, we study a class of self-exciting point processes. The intensity of the point process has a nonlinear dependence on the past history and time. When a new jump occurs, the intensity increases and we expect more jumps to come.…
The opportunity of occurrence of entropy oscillations around of a stationary state in linear and nonlinear processes is theoretically shown. The new mechanism of global tendencies appearance is described.
Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This paper uses a recent advance in stationary count time series to develop a general seasonal count time…
This article present a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade. One multiplicatively…
We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…